Tuesday, October 31, 2017

How Not to Title your Dissertation

So I just had to look up my official dissertation title on my grad school's website and....well, here's a little piece of advice I would give to my past self. (The 'do' example comes from the excellent Johann Frick)
MoH&H title

"'Making People Happy, Not Making Happy People': A Defense of the Asymmetry Intuition in Population Ethics"  <-- conveys the core of the view being advocated, what's controversial about it, and why it's appealing, in a punchy and fairly concise way


"The Marriage of Rationalism and Empiricism: A New Approach to the Access Problem." <-- draws attention to question of whether dissertation does anything new in a defensive "protesting too much" way that invites a negative answer, compares self to William Blake and/or God.

Sunday, October 29, 2017

Access to reference magnets: a bitter pill you’ve already swallowed?

[This post proposes a defense of a famous defense of naive scientific realism against a famous antirealist challenge.  So, sorry that I'll have to speed through certain classics to get to the action in a timely fashion (and I'll try to add explanatory links later). 

Also, Ted Sider may have scooped me re: this proposal in Writing the Book of the World section 3.2 (I go back and forth about how to interpret him). But, regardless of priority, I'm shouting about it on the internet now because I'd like to see more uptake.]

Hillary Putnam raised a model theoretic challenge to the commonplace realist idea that `even in the ideal limit of scientific investigation' certain aspects of our best theory of the world could be wrong. David Lewis responded by invoking "reference magnets" (i.e., intrinsically eligible concepts/joints in nature) as a response to this challenge. The idea is that some concepts are more intrinsically eligible candidates for the meaning of words than others. So, it can be correct to interpret someone as meaining plus vs Kripke's quus, or electron vs. electron-that-an-ideal-observer-starting-on-earth-could-discover, even if this involves attributing them slightly more false beliefs.

Swinging back on behalf of Putnam, Tim Button and Jared Warren press a kind of access problem for fans of reference magnets. Suppose that there really are intrinsically eligible joints in nature as Lewis argues. How could creatures like us have come to recognize where these joints are, well enough to know when there is a single reference magnetic joint for our use of some word to defer to?

I think this challenge is worth taking seriously and may point out a bitter pill* which the realist/friend of reference magnetism must swallow. But I want to suggest that this bitter pill may already be part of the larger bitter pill nearly everyone has already swallowed in taking our intuitions about how to do scientific induction at face value. That is, accepting reference magnets doesn't land us with any more of an access problem than we already face in rejecting Humean skepticism about induction.

To see what I mean, consider Nelson Goodman's picture of scientific induction. When we do scientific induction, we don't treat all concepts equally. We currently take some predicates (and relations and functions etc) to be more projectable than others, e.g., green v.s grue. And (Goodman notes) we do a kind of induction about how to do induction, letting experience and reflection change our beliefs about which predicates are projectable. So (in effect) we dogmatically presume both that certain predicates are more projectable than others, and that that certain ways of letting experience change our beliefs about which predicates are projectable are reliable. And plausibly, taking scientific induction at face value requires doing something like this.

But maybe the friend of reference magnets can say that access to these facts about what's joint carving (in the sense of being specially friendly to induction) is all they need for access to reference magnets. If the reference-magnet-fan's doctrine identifies being an intrinsically eligibile concept in the sense of reference magnetism with being an intrinsically eligible concept for the purposes of scientific induction (as, e.g. Sider does and I essentially want to**), then it seems that accepting this doctrine create any extra intuitive access worries.

*[i.e., Perhaps they must embrace a rather depressing picture of the human condition, on which `justified’ reasoning (to the extent that we have any such thing) involves going along dogmatically assuming that certain methods for detecting intrinsically eligible concepts/reference magnets are tolerably accurate (and then being lucky enough to be right about this)]

**[I think one tiny refinement answering Hawthorne's problem about Europe and the Ural Mountains discussed on pg 39 of WTBOTW is needed, but that this makes no difference to the access problem stuff above. More on this in a later post]

Saturday, October 28, 2017

Trivializing Benacerraf and Monstrous Moonshine

[note: Sorry that this post is a little wordy. I'm trying to get back into blogging, and forcing myself to post stuff I'm not quite happy with is part of that. Also see this paper for a way more detailed and less aggro take on this issue.]

Remember that the access problem (aka the Benacerraf problem) for realists goes something like this: If moral/mathematical/etc realism is true, how can human accuracy and reliability about moral/mathematical facts be anything but a miracle or a mystery?

People like Justin Clarke-Doane and perhaps David Enoch, (call them The Trivializers) have been suggesting that we can answer all legitimate access worries besetting for realists about necessary domains like mathematics morals etc. just by “stapling together” two things to explain why we couldn't have easily been wrong (and providing a similarly trivial explanation for the sensitivity of our I won't discuss here):
  • an  explanation (e.g.historical or evolutionary) for why we reliably believe certain moral/mathematical/etc claim,
  • the fact that these claims are necessary truths
So, for example, a classic platonist might try answer access worries by explaining human reliability about mathematics like so:

TRIV: Mathematicians reliably believe truths because they reliably believe only those mathematical claims which can be proved in a certain formal system (e.g. ZFC) and this formal system is (necessarily) truth preserving w.r.t. the platonic mathematical objects.

Such an explanation is not likely to satisfy anyone who feels an intuitive access worry. For TRIV just explains one intuitively mysterious match between human psychology and objective which intuitively “cries out for explanation” (our acceptance of theorems that match whats going on in Plato's heaven) by positing another such mysterious match (our acceptance of axioms that match what's going on in Plato's heaven).

But it does (in some sense) suffice to explain the safety of human beliefs by deriving our reliability about realist facts concerning the relevant domain (i.e., that in all close possible worlds, our beliefs about these domains match up with the truth) from more general premises which the realist (if not their deflationary opponents) accepts.

And I take Trivializers to be suggesting that our intuitions that certain regularities involving necessary truths "cry out for" explanation in a deeper/more unified sense, which mere deductions of reliability/safety/sensitivity like TRIV need not provide, is an illusion.

There are two reasons why I don't buy this.

First, conceptually analyzing anything (from tablehood to justice) is infamously hard, but there are plenty of good paradigms for how to think about ”crying out for explanation” which seem to apply equally well to necessary and contingent regularities (e.g., norms that say we should preferring theories that have fewer degrees of freedom and or Kitcher’s idea of scientific explanation as unification).

Much more importantly though, embracing the Trivializers' position seems to have deeply implausible revisionary consequences for mathematical practice, since mathematicians sure seem to think that some regularities involving necessary truth truths can cry out for (non-trivial) explanation.

For example, consider this quote from a popularizing article about the history of John Conway's `Monstrous Moonshine' conjecture.

``Strangely enough, [the j- function]’s first important coefficient is 196,884, which McKay instantly recognized as the sum of the monster’s first two special dimensions.
Most mathematicians dismissed the finding as a fluke, since there was no reason to expect the monster and the j-function to be even remotely related. However, the connection caught the attention of John Thompson, a Fields medalist now at the University of Florida in Gainesville, who made an additional discovery. The j-function’s second coefficient, 21,493,760, is the sum of the first three special dimensions of the monster: 1 + 196,883 + 21,296,876. It seemed as if the j-function was somehow controlling the structure of the elusive monster group.'’’

Note that mathematicians already had separate proofs of facts about the j-function and monster group (and hence an `explanation' of for the match between these facts of the kind which TRIV provides, i.e., a deduction, from more general premises, of the fact that this relationship holds in all close possible worlds). But (once this match between apparently unrelated domains proved striking enough) they expected to find some further/deeper unifying explanation and this expectation guided choices for further research.

So I'm prima facie pretty suspicious of the idea that felt intuitive demands for unifying/satisfying/non-trivial explanations of regularities involving necessary truths are generally misguided. But maybe I'm not being charitable to Clarke Doane and/or he can find some way of separating the "this regularity cries out for further explanation" intuitions he wants to dismiss as unreliable from those which obviously do good work in mathematics.